The 30-year-old could lose his number one ranking to Spain’s Rafael Nadal and is a doubt for the US Open, which starts on 28 August.

“I’m continuing to work hard on the court with the aim of being in New York,” said Murray.

“I won’t be playing in Cincinnati as I continue my recovery – I always enjoy playing there and I look forward to returning next year.”

The US Open – the final Grand Slam of the season – runs until 10 September in New York.

Murray, who has held the number one ranking since November, will be overtaken by Nadal, 31, if the Spaniard reaches the semi-finals of the Rogers Cup.

Top seed Nadal faces Croatia’s Borna Coric in his second round tie in Montreal later on Wednesday.

Nadal will also be the top seed in Cincinnati, which starts on 13 August, with Wimbledon champion Roger Federer the second seed – the first time the pair have been the top two seeds at the event since 2009.